Transmission line matching



Sept; 14, 1943.

sQcAR-rER' Re. 22,374 TRANSMISSION LI ENE MATCHING Original Filed March 14,1959

- uvvszvz-oa. PHILIP s. CARTER ATTORNEY.

Reiuue d Sept. 14, 1943 UNITED STATES PATENT f OFFICE TRANSMISSION LINE MATdHING I Philip S. Carter, Port Jeiierson, N. IL, assignor to Radio Corporation of America, a corporation of Delaware Original No. 2,213,465; dated February 17, 1942,

Serial No. 261,745, March 14, 1939. Application for reissue May 30, 1942, Serial No. 445,227

8 Claims.

The present invention relates to a means for matching a transmission line having a predetermined value of surge impedance with an antenna or a load circuit having a widely diflferent value of impedance.

More particularly, the present invention re- I and means for matching a transmission line to a load circuit by means of which the above mentioned difllculty is, for most practical purposes.

. eliminated.

An object of the present invention is to match the impedance or an antenna having a broad frequencycharacteristic to the surge impedance of a. transmission line without destroying the frequency characteristic of the antenna.

Another object of the present invention is to provide matching means for the impedance of an antenna to the surge impedance of a transmission line having a value of surge impedance widely different from the impedance of the antenna without restricting the frequency band width of the antenna. I

Still another, object of the present invention'is to provide means for matching the impedanc of one radio frequency translating means to the impedance of another translating means having a value of impedance widely different from the impedance of the first translating means without restricting the frequency band width over which said means are operative.

Briefly, my invention involves the use of an even number of quarter wave line sections in series between the antenna or other load and the transmission line or other translating means, the ratio of impedance of said sections bearing such a relationship to the ratio of the impedances of the transmission line and antenna that the transmission line is matched to the load over a comparatively wide band of frequencies.

For a more complete understanding of the invention, reference may now be made to the following detailed description which is accompanied by drawing in which Figure 1 illustrates a method of matching a transmission line to a load circuit having a value iii-impedance difierent from the impedance of the transmission line and. is shown only for the purposes or explanation; Figure 2 illustrates diagrammatically an example of the present invention wherein 2 quarter wave line sections connected in series are interposed between the transmission line and the load.

Figure 1" shows a transmission line having a surge impedance indicated by Zoe, connected to a load having an impedance Zn equal to sixteen times the impedance Zoo. Connected between the transmission line and load is shown-a matching section M having a length equal to a quarter of the length of the operating wave and having a surge impedance Zn equal to four times the surge impedance Zoo or the transmission line.

In Figure 2 the same transmission line and same load are shown as in Figure l. Interposed between the transmission line and theload are two impedance matching sections M1 and M2 connected in series and each having a length equal to a quarter of the length of the operating wave at the midband frequency.

According to my invention the surge impedance Z01 of the first matching section M1 is made equal to the one-quarter power of the impedance ratio between the transmission line and the load or, in the specific example shown in Figure 2, twice the surge impedance of the trans-. mission line.. The surge impedance Z02 of the second matching section M2 is made equal to the three-quarter power of the impedance ratio between the transmission lin andthe load or, in the specific example shown in Figure 2, equal to eight times theimpedance of the transmission line.

While I have shown the use of two matching sections in Figure 2 it is to be clearly understood that a number of matching sections may be any even number in accordance with the invention.

In the following detailed mathematical theory of broad band impedance matching according to my invention, it sections will be considered each section being equal to a quarter of the length of the operating wave at th midband frequency. The number n will be considered even in accordance with the invention. Usually two sections (n=2) are suflicient.

If R is the impedance ratio to be changed and if Zoi, Z02 Ztm are the surge impedances of the quarter wave lines and Zoo the surge impedance of the main line, we make:

I a 2k-l QZE=R(I)ZQ=R('Z7I)EUE=R -21? Z00 Z Z09 where R: is the ordinal number of a particular section. When n=2 for simplicity.

At the mid-band frequency, where the length Then comes of eachsection is exactly 'X/4, the section Z e The input impedance Zn of section M1 looking changesthe impedance from RZoo to h from the transmission line TL then becomes:

R l mum:

Let p=the ratio of increase in frequency to the t mid-band fr qu yv t =Zoo exp (i0) which indicates a perfect match I P= phase angle introduced into the input impedance of one line section is almost perfectly cancelled where Af=ehan e i f equ cy fi by an opposite phase shift due to the action of Af with the approximationsmade. In any case the frequencythe other section when working ofllthe mid-band v frequency. There is, however, a small decrease 211 21rfl in the final input resistance. a 9=11I16 T =7 A specific case will now be dealt with using the l value iven in the drawin Assume a loadof. where l =line length x=wave length, f=frequency 16 i the surge impedagce or a main 1m e to and light" I a be matched-thereto. If the matching is done in one step a quarter wave line is used as shown in 1r 1r Figure 1 with a surge impedance equaltoAZtt wherezto is the surge impedance of the main radians 7 h line. i If the frequency is 5 percent "high the in- Let K,=(K) exp (7 =coefliclent of reflection put impedance becomes w on a line section where (Ky is the magnitude, Zoo(1.05)/16.33=Zno(1.006+10.296) the phase angle and exp (w) Thus it will be seen that there is introduced a K defined by the relation h reactive component equal to about 30% of the Z Z a resistive component. This causes a reflection on the main line 01 about 15 percent, whichis three where Znis the load impedance and Z.) the sur e almwable 5% in televisiim impedance of the transmission line. p

From fundamental relations the m imped Now suppose thetransformation is done in two ance z or any line section is steps in accordance Pith the invention and as shown in Figure 2. In this case Zo1=(16) "190 220a and Zoa =(16) Zot=Zoo. Calculation, witht For matching section M: with zn=rtwz e d 40 the final input impedance at a frequency 5 1 I load R200 cent high to be Zoo 1: 0'-.9I8/0l 08.' The reactive 1 I a f l RZ Rx 1/ v component is negligible. The slight miss-match 155W: Rm exp (jO) v v in the resistive component produces a reflection or 1.1% on the mainline, and its eflect is prac-.

and the input impedance Z1: 0! section M: betically negligible.

v While I have shown and particularly described 1 i several embodiments of myinvention, itis tobe' 2: a a distinctly understood that 'my'invention is not I limited thereto '1) t that thi' n When pr is not great so that cos plr 1 and sin u modifications W1 J scope of my invention may be made.

p1r 1r and pal the above becomes v I claim: t l V Z Z (m) (K9 Q") :9 1. In combination, a wide band antenna system impedance of said antenna being Rtimes the r n of matching line sections connected in series and a transmission line connected thereto, the lei 220] surge impedance Zoo of said line, an even number,

270:) t and interposed between said antenna and trans- Z exp mission line, each of said sections having a g 1+(Ke) -09 length equal to one-quarter of the length or the v i 6 operating wave at midband frequency and havv I v I x Rx irigtsfi rgeimpedancesoi'zonzes .azn theratio' r v y 0 es eim danceoie i impedance constitutes the load for the an m m o md'mflons tothat otthelinebeingex esn section Ml having a surge impedance Z01. 1;; for pr relation thisfsection is given by. l h I .g n v I i V a a -1'1 a 4 up 2 R where It denotes the ordinal number-pi the 2 u .112 -1 Z a section. l a w p J T- v 2. In combinationaradio i'requencyloadand.;, B 1 a transmissibn-line connected therein, the im-' -g B R 'Pedanceotsaid loadbeingRtimesthesurgeima 1 exp pedance Zoo 01' saidline, an even number n of RR 1 R*+1 t matching line sections connected in series and v 2 i t '75 interposed between said radio frequency load and where k denotes the ordinal number of the sec- I tion. i

each section being less than one adjacent impedance and greater than the other adjacent im pedance.

6. In combination with'a wide band antenna and a transmission line, of means for matching said transmission line to said antenna over said 3. In combination, a radio frequency load and I a transmission line connected thereto, the impedance of said load being R times the surge impedance of the transmission line, a pair of matching line sections connected in series and interposed between said load and transmission line, each of said sections having a length equal to one-quarter of the length of the operating wave at midband frequency, the. section adjacent said transmission line having an impedance R times the surge impedance of said transmission line and the second section having an impedance R times the surge impedance of said-transmission line.

4. In combination with a wide band antenna system and a transmission line connected thereto, the impedance of said antenna being R times the surge impedance of the transmission line, of means for matching said transmission line to said antenna over said wide band comprising a pair of matching line sections connected in series and interposed between said antenna and transmission line, each of said sections having a length equal to one-quarter of the length of the operating wave at midband frequency, the section adjacent said transmission line having an impedance R times the surge impedance of said transmission line and the second section having an impedance R times the surge impedance of said transmission line.

5. In combination, a radio frequency load operable, over a wide band of frequencies and a quencies removed from midband the reactance introduced by each section is counterbalanced by an opposite reactance introduced by another of said sections, the surge impedance of each of said sections having values between the limits-determined by the impedances of said load and said transmission line, the surge impedance oi wide band comprising a pair of seriesconnected matching sections interposed between said transmission line and antenna, each having a length equal to one-quarter of the length of the operating wave at midband frequency, the surge impedance of each of said sections being so proportioned with respect to the ratio of said antenna impedance to line impedance that at frequencies removed from midband the reactance introduced by one section is counterbalanced by an equal and an opposite reactance introduced by the other of said sections,the surge impedance of each of said sections having values between the values of impedance of said antenna and the impedance of said transmission line, the surge impedance of each section being. less than one adjacent impedance and greater than the other adjacent impedance.

7. In combination, a pair of radio frequency translating elements connected together, the 1mpedance of one of said elements being R times the surge impedance Zoo of the other of said elements, an even number n of matching line sections connected in series and interposed between said eleby the relationship where ,k denotes the ordinal number of each section.

8. In combination, a first radio frequency translating means and a second translating means connected thereto, the impedance of said first translating means being R times the surge one-quarter of the length of the operating frequency at midband frequency, the 'section adjacent said second translating means having an impedance RV times the surge impedance of said second translating means and the second section having an impedance R times the surge impedance of said second translating means.

PHILIP S. CARTER. 

